During the first week of my placement I was lucky enough to attend a math conference that was developing the new pedagogy for teaching mathematics to elementary school students in Durham District School Board. The conference was attended by teachers, administrators and board officials as well as people from the numeracy and literacy secretariat. The day was divided into half and in the morning we developed a lesson to be taught that day using the new teaching methods. That afternoon we taught the lesson and then re-convened to discuss the successes and failures.
The new methodology is a very hands on approach to mathematics. It relies heavily on self-discovery and the usage of manipulatives to allow students to develop their own understanding of the problem. I could easily see the links between the things talked about at the conference and our Problem Based Learning class, so I decided to use a hybrid model of my own last week in my own classroom.
My grade 6's had just finished a test on geometry so I decided I'd approach fractions as the next topic in mathematics. I designed a diagnostic assessment to give to them in two parts to determine where we we're at. The first day students were in their table groups and given the following problems: 1/4 = ?% and 50% = ? Fraction. Together using manipulatives they had to write down on their group's chart paper (with a different colour marker per students for accountability) as many ways as they could to solve this problem. This worked surprisingly well, my students knew more than I had expected and this let me re-frame a new problem the next day of a higher degree of difficulty.
That second day I gave them a handout individually to prove the following statement: 2/5 = 40% = 0.40 The students could use any manipulatives available to them and were encouraged to write their responses to show their thinking. Some students decided they needed to investigate more and referenced their textbook and other math materials around the classroom. Others used the computer to search for help. In the end the class came up with 7 or 8 ways to prove this statement at a grade 6 expectation level. The openness and richness of the question gave them lots of room to demonstrate what they knew or what they learned the day before. It also required them to search out or explore for more information as decimals were something fairly new to them in equivalent forms.
Through my observations of my students as well as reading over their work I have been able to plan forward in our fractions unit to target those areas that are lacking to build up their skill set. The students loved the freedom of the activity, they were engaged, on task and produced a high quality level of work. This constructivist style of learning coupled with the big open problems yields great results within the classroom because it allows students the freedom to utilize their own learning strategies to discover knowledge. It will be very interesting to see how much they can retain next week from these tasks going forward.
My goal is to create a similar open ended problem for a formative assessment next week in which we will build a rubric of expectations together. This will allow the process to become full circle and will provide me a chance to formally assess the student's abilities in this mathematics unit.
By: Richard Bishop
During the first week of my placement I was lucky enough to attend a math conference that was developing the new pedagogy for teaching mathematics to elementary school students in Durham District School Board. The conference was attended by teachers, administrators and board officials as well as people from the numeracy and literacy secretariat. The day was divided into half and in the morning we developed a lesson to be taught that day using the new teaching methods. That afternoon we taught the lesson and then re-convened to discuss the successes and failures.
The new methodology is a very hands on approach to mathematics. It relies heavily on self-discovery and the usage of manipulatives to allow students to develop their own understanding of the problem. I could easily see the links between the things talked about at the conference and our Problem Based Learning class, so I decided to use a hybrid model of my own last week in my own classroom.
My grade 6's had just finished a test on geometry so I decided I'd approach fractions as the next topic in mathematics. I designed a diagnostic assessment to give to them in two parts to determine where we we're at. The first day students were in their table groups and given the following problems: 1/4 = ?% and 50% = ? Fraction. Together using manipulatives they had to write down on their group's chart paper (with a different colour marker per students for accountability) as many ways as they could to solve this problem. This worked surprisingly well, my students knew more than I had expected and this let me re-frame a new problem the next day of a higher degree of difficulty.
That second day I gave them a handout individually to prove the following statement: 2/5 = 40% = 0.40 The students could use any manipulatives available to them and were encouraged to write their responses to show their thinking. Some students decided they needed to investigate more and referenced their textbook and other math materials around the classroom. Others used the computer to search for help. In the end the class came up with 7 or 8 ways to prove this statement at a grade 6 expectation level. The openness and richness of the question gave them lots of room to demonstrate what they knew or what they learned the day before. It also required them to search out or explore for more information as decimals were something fairly new to them in equivalent forms.
Through my observations of my students as well as reading over their work I have been able to plan forward in our fractions unit to target those areas that are lacking to build up their skill set. The students loved the freedom of the activity, they were engaged, on task and produced a high quality level of work. This constructivist style of learning coupled with the big open problems yields great results within the classroom because it allows students the freedom to utilize their own learning strategies to discover knowledge. It will be very interesting to see how much they can retain next week from these tasks going forward.
My goal is to create a similar open ended problem for a formative assessment next week in which we will build a rubric of expectations together. This will allow the process to become full circle and will provide me a chance to formally assess the student's abilities in this mathematics unit.